New strategy to improve the dotted board model for solving two dimensional cutting and packing problems

In this paper, the dotted inner-fit raster (DIFR) is used to build an improved dotted board model, denoted as (IDBM). The DIFR is a new concept can be utilized to define the feasible solution matrix of each item and to define the dotted no-fit raster in the two dimensional cutting and packing problems. It is found that using DIFR to build the IDBM instead of using regular dotted board model (DBM) has many benefits, such as that IDBM can be used for any shape, not only polygon, it reduces the number of constraints in the optimization model, and it makes the number of decision variable depends on the number of piece types not on the total number of pieces. Consequently, seven instance groups; 6 from literature and one from real work, with maximum piece types of 8 and with number of pieces ranging from 24 to 60 were optimally solved in acceptable computational time by IDBM, which was impossible by older concepts.

Automated summary

The paper introduces a new concept - Dotted Inner-Fit Raster (DIFR) for building an improved Dotted Board Model (IDBM). Compared to traditional Dotted Board Model (DBM), IDBM is applicable to any shape of problem, reduces the number of constraints in the model, and has decision variables depending on the number of piece types.